The quality of offset printing depends substantially on the uniformity of application of ink and wetting liquid. Many efforts have been made to obtain as good a result as possible while using a simple construction. To transfer ink from an ink supply trough on the plate cylinder which is to be inked, it has been customary to provide a number of transfer rollers, ink grinding cylinders, for example rollers which are axially oscillating, and to utilize several ink application rollers. The effort which has been made was directed to the aim to provide a film of ink which has the required uniformity and thickness. It is desirable to simplify offset printing machines and to reduce the space requirements of the inking system and all the rollers in the ink train. Difficulties arise due to the mutually contradictory requirements--for uniformity a large number of rollers, and for simplicity as low a number of rollers--which has been discussed in the literature, for example, see German Patent Disclosure Document DE-OS 29 16 291.